Carmen Vierheilig

Interplay between dissipation and driving in nonlinear quantum systems

In this thesis we investigate the interplay between dissipation and driving in nonlinear quantum systems for a special setup: a flux qubit read out by a DC-SQUID - a nonlinear quantum oscillator. The latter is embedded in a harmonic bath, thereby mediating dissipation to the qubit.
Two different approaches are elaborated: First we consider a composite qubit-SQUID system and add he bath afterwards. We derive analytical expressions for its eigenstates beyond rotating wave imation (RWA), by applying Van Vleck perturbation theory (VVPT) in the qubit-oscillator coupling. The second approach is an effective bath approach based on a mapping procedure, where SQUID and bath form an effective bath seen by the qubit. Here the qubit dynamics is obtained by applying standard procedures established for the spinboson problem. This approach requires the knowledge of the steady-state response of the dissipative Duffing oscillator, which is studied within a resonant and n offresonant approach: The first is applicable near and at an N-photon resonance using VVPT beyond a RWA. The second is based on the exact Floquet states of the nonlinear driven oscillator.
The dissipative qubit dynamics is described analytically for weak system-bath coupling and agrees well for both approaches. We derive the effect of the nonlinearity on the qubit dynamics, on the Bloch-Siegert shift and on the vacuum Rabi splitting.
Beigaben:23 farb. Illustrationen
Einbandart:Broschur klebegebunden
Format:17 x 24 cm
Gewicht:427 g